Sequential prediction is an essential component of Artificial Intelligence (AI) and Machine Learning (ML) in a number of domains. In this paper, we analyze the performance of sequential prediction algorithms that are used to predict the next event in smart environments. We first employ three sequential prediction algorithms, namely LZ78, Active LeZi (ALZ) and the Sequence Prediction via Enhanced Episode Discovery (SPEED) to build sequential trees, and then an efficient prediction algorithm with different window lengths is applied to these trees to predict the next sensor event for a sequence of activities. The sequential algorithms are tested with different window lengths for a dataset consists of 25 sensors. The results show that the best prediction accuracy is achieved by SPEED with a peak accuracy of 92.86%, but with higher storage requirement compared to LZ78 and ALZ.